The present invention relates generally to dialysis clearance. More particularly the invention relates to a method of estimating a process efficiency of a dialysis system according to the preamble of claim 1, a method of estimating a whole body clearance ratio according to the preamble of claim 6, corresponding computer programs and computer readable media according to claims 11 and 13 respective 12 and 14, an apparatus adapted to estimate a whole body clearance ratio according to claim 16, as well as use of this apparatus according to claim 17. The invention also relates to a method of performing a dialysis treatment program according to the preamble of claim 15.
Generally in dialysis, there is a large need to better understand the differences between patients, and what factors determine the achievable efficiency of the dialysis treatment in the individual patients. In theory, a number of different parameters may be used to characterize a dialyzer's capacity to filter waste products from a patient's bloodstream and restore the normal constituents of his/her blood. For example, models for solute concentrations in the different body parts may be used. It is also possible to characterize patients by measurable parameters, which in turn, may be used to improve the efficiency of the dialysis treatments.
A good model to use in order to understand the process of dialysis for cleaning the body from a solute is the so-called regional blood flow model for the solute distribution in the body, which was developed by Daugirdas and Schneditz. Urea is a common marker molecule for the description of the dialysis progress, and will be used for the following discussion for this purpose. However, the same discussion may also be applied to other solutes, such as creatinine, glucose, phosphate and other ions. According to one model, the human body includes two urea containing pools; one large pool of volume VL, which is perfused by a relatively small blood flow QL, and one small pool of volume VH, which is perfused by a relatively large blood flow QH, see FIG. 1. The small pool of volume VH represents the blood in the internal organs, such as the liver etc., and the large pool of volume VL represents blood located in the muscles, the skin and the like. Due to the comparatively large blood flow QH to the small pool of volume VH, this pool will be much more efficiently depurated than the large pool of volume VL. Thus, after an initial transient, the concentration of urea CH in the small pool of volume VH will be lower than the concentration of urea CL in the large pool of volume VL. Before returning to the heart η, the blood from the two pools VL and VH will be mixed, and a mixed venous urea concentration Cmv therefore becomes a weighted mean value of the two pool concentrations CL and CH, with the respective flow weights QL and QH, according to the following:
      C    mv    =                              Q          L                ·                  C          L                    +                        Q          H                ·                  C          H                                    Q        L            +              Q        H            
The denominator here represents the total blood flow QL+QH. Note that the mean value Cmv falls between the two pool concentrations CL and CH. However it will be closer to the concentration of urea CH in the small pool of volume VH because its weight QH is larger than QL. Before reaching the heart η, the mixed venous blood will also mix with partly cleaned blood from the dialyzer 130, so that the concentration of urea in the heart η which is equal to a concentration Cb returning to the access and the dialyzer, will be lower than all other concentrations.
When discussing the depuration of the whole body it is of interest to also discuss the mean concentration of urea in the whole body. This is sometimes referred to as the equilibrated concentration Ceq, since it is the concentration which would be the result if the body were left to equilibrate the pool concentrations CL and CH. In our regional blood flow model, the equilibrated concentration Ceq is:
      C    eq    =                              V          L                ·                  C          L                    +                        V          H                ·                  C          H                                    V        L            +              V        H            
The equilibrated concentration Ceq will also fall between the pool concentrations CL and CH. However, it will be closer to the concentration of urea CL in the large pool of volume VL because of the volume VL being larger than the volume VH. Consequently, we obtain the relationship:CL>Ceq>Cmv>CH>Cb 
Clearance is an entity which is used to describe the efficiency of the depuration process. More precisely, clearance is defined as the removal rate divided by the concentration of the substance in the fluid to be cleaned. Normally, a dialyzer clearance K, which is used to characterize dialyzers at different flow conditions, is defined as the removal rate divided by the concentration Cb, i.e. the concentration in the blood returning from the heart-lung system to the access and the dialyzer. A part of the cleaned blood from the dialyzer which is mixed with the blood returning from the body goes from the heart and enters directly into the dialyzer again. This is called cardiopulmonary recirculation, and is the reason why blood entering the dialyzer has a lower concentration (i.e. Cb) than the blood returning from the body. A so-called effective clearance Keff is instead defined as the removal rate divided by the mixed venous concentration Cmv, and is a better measure of the effective depuration of the patient. The effective clearance Keff can be estimated if the removal rate is measured either on the blood side or on the dialysate side of the dialyzer, and the mixed venous concentration (or the systemic blood concentration) Cmv is measured by stopping the blood pump during an interval (say 1 minute) to let the effect of the cardiopulmonary recirculation disappear before a blood sample is drawn. Another simple method to estimate the effective clearance is to measure the effect in the outlet dialysate conductivity of a step in the inlet dialysate conductivity, for instance according to the procedures proposed in the documents EP 547 025, EP 658 352 and U.S. Pat. No. 6,217,539.
However, a still better measure would be to describe the cleaning of the whole body equilibrated concentration Ceq. This so-called whole body clearance Kwb (or Keq) is defined as the removal rate divided by the equilibrated concentration Ceq. Moreover, due to the relationships between the corresponding urea concentrations, we obtain the following relationships between the clearances:K>Keff>Keq 
Since it is relatively difficult to measure the pool concentrations CL and CH there is no straightforward way to measure the equilibrated concentration Ceq, and consequently, the whole body clearance Kwb is also difficult to estimate. One possibility to measure the equilibrated concentration Ceq is to wait until the concentrations have equilibrated after the treatment. However, this takes relatively long time (half an hour up to one hour) and is therefore impractical.
The interest in the whole body clearance Kwb originates from the fact that this measure describes the cleaning effect of the dialyzer on the body, whereas the dialyzer clearance K and the effective clearance Keff constitute descriptions of the cleaning capacity of the dialyzer and the dialyzer together with the heart-lung system η and λ respectively. The dialyzer clearance K is known from the dialyzers data sheet, and the relationship between this measure and the effective clearance Keff is given by the expression:
      K    eff    =      K          1      +              K        /        Q            where Q is the total systemic blood flow, i.e. Q=QL+QH. Unfortunately, the relationship between the effective clearance Keff and the whole body clearance Kwb is much less trivial.
It is nevertheless possible to study the theoretical relationship between the pool concentrations CL and CH. Setting up a mass balance equation for each of the two pools of volume VL and VH leads to a system of two coupled first order differential equations for the concentrations CL and CH. If we include the effect of a constant ultrafiltration rate, the pool volumes VL and VH will decrease linearly over time, and the differential equations for the concentrations CL and CH will have variable coefficients.
Daugirdas and Schneditz have managed to solve these equations for the case when the urea generation in the pool volumes VL and VH was included. Daugirdas and Schneditz studied the impact on the rebound of urea after treatment, i.e. the magnitude of the equilibration of urea concentrations after the treatment. However, the volumes VL and VH were allowed to vary, which in turn, led to a non-steady state relationship between the pool concentrations CL and CH. Thus, a reliable estimate of the whole body clearance Kwb could not be obtained.
The U.S. Pat. No. 6,258,027 discloses a method and a device for calculating dialysis efficiency with respect to a mass exchange of a solute in a fluid. However, no measure is determined which reflects the whole body clearance of the dialyzer on a patient.